Estimating the Marginal Law of a Time Series with Applications to Heavy Tailed Distributions
This article addresses estimating parametric marginal densities of stationary time series in the absence of precise information on the dynamics of the underlying process. We propose using an estimator obtained by maximization of the "quasi-marginal" likelihood, which is a likelihood written as if the observations were independent. We study the effect of the (neglected) dynamics on the asymptotic behavior of this estimator. The consistency and asymptotic normality of the estimator are established under mild assumptions on the dependence structure. Applications of the asymptotic results to the estimation of stable, generalized extreme value and generalized Pareto distributions are proposed. The theoretical results are illustrated on financial index returns. Supplementary materials for this article are available online.
(This abstract was borrowed from another version of this item.)
|Date of creation:||2011|
|Contact details of provider:|| Postal: Bâtiment ENSAE, 5 rue Henry LE Chatelier, 91120 Palaiseau|
Phone: 01 41 17 60 81
Web page: http://www.crest.fr
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Boubacar Mainassara, Y. & Carbon, M. & Francq, C., 2012.
"Computing and estimating information matrices of weak ARMA models,"
Computational Statistics & Data Analysis,
Elsevier, vol. 56(2), pages 345-361.
- Boubacar Mainassara, Yacouba & Carbon, Michel & Francq, Christian, 2010. "Computing and estimating information matrices of weak arma models," MPRA Paper 27685, University Library of Munich, Germany.
- Cotter, John, 2007. "Varying the VaR for unconditional and conditional environments," Journal of International Money and Finance, Elsevier, vol. 26(8), pages 1338-1354, December.
- Cotter, John, 2004. "Varying the VaR for Unconditional and Conditional Environments," MPRA Paper 3483, University Library of Munich, Germany.
- John Cotter, 2011. "Varying the VaR for Unconditional and Conditional Environments," Papers 1103.5649, arXiv.org.
- John Cotter, 2011. "Varying the VaR for Unconditional and Conditional Environments," Working Papers 200419, Geary Institute, University College Dublin.
- Shiqing Ling & Michael McAleer, 2010. "A general asymptotic theory for time-series models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(1), pages 97-111.
- Shiqing Ling & Michael McAleer, 2009. "A General Asymptotic Theory for Time Series Models," CIRJE F-Series CIRJE-F-670, CIRJE, Faculty of Economics, University of Tokyo.
- Jansen, Dennis W & de Vries, Casper G, 1991. "On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 18-24, February.
- Dennis W. Jansen & Casper de Vries, 1988. "On the frequency of large stock returns: putting booms and busts into perspective," Working Papers 1989-006, Federal Reserve Bank of St. Louis.
- Gamini Premaratne, 2005. "A Test for Symmetry with Leptokurtic Financial Data," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(2), pages 169-187.
- Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394-394.
- Einmahl, John H. J. & Li, Jun & Liu, Regina Y., 2009. "Thresholding Events of Extreme in Simultaneous Monitoring of Multiple Risks," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 982-992.
- Stephen J. Taylor, 2007. "Introduction to Asset Price Dynamics, Volatility, and Prediction," Introductory Chapters,in: Asset Price Dynamics, Volatility, and Prediction Princeton University Press.
- Francq, Christian & Roy, Roch & Zakoian, Jean-Michel, 2005. "Diagnostic Checking in ARMA Models With Uncorrelated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 532-544, June. Full references (including those not matched with items on IDEAS)